Can standard deviation ever be greater than the range? I am thinking "no", but can't explain why. Thanks!!

The mean of the data has to be inside the range of the data, so no single term (before being squared) in the sum can exceed the range. This makes it easy to show that the standard deviation has to be smaller than the range.

A more interesting question might be to show that the standard deviation is always less than or equal to half the range.